High order discretization methods for spatial-dependent epidemic models
| Autor: | Takács, Bálint, Hadjimichael, Yiannis |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Math. Comput. Simulation 198 (2022), pp. 211-236 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.matcom.2022.02.021 |
| Popis: | In this paper, an epidemic model with spatial dependence is studied and results regarding its stability and numerical approximation are presented. We consider a generalization of the original Kermack and McKendrick model in which the size of the populations differs in space. The use of local spatial dependence yields a system of partial-differential equations with integral terms. The uniqueness and qualitative properties of the continuous model are analyzed. Furthermore, different spatial and temporal discretizations are employed, and step-size restrictions for the discrete model's positivity, monotonicity preservation, and population conservation are investigated. We provide sufficient conditions under which high-order numerical schemes preserve the stability of the computational process and provide sufficiently accurate numerical approximations. Computational experiments verify the convergence and accuracy of the numerical methods. Comment: 34 pages, 4 figures, 4 tables |
| Databáze: | arXiv |
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